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Confronting imperfect detection: behavior of binomial mixture models under varying circumstances of visits, sampling sites, detectability, and abundance, in small-sample situations
Yuichi Yamaura
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Volume 12 (2013) Issue 2 Pages 73-88

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Binomial mixture models (BMMs) have been increasingly applied to account for imperfect detection and to estimate abundance from count data, but their performance has not been thoroughly evaluated. Here, I conducted simulation experiments to examine parameter estimates in BMMs under various situations. I generated data by assuming that abundance followed a Poisson distribution with an expected value λ and that the number of detected individuals followed a binomial distribution with an individual detection probability p. In simple simulations without covariates for λ and p, when the number of sampling sites (n) was between 20 and 160, BMMs could recover λ and p under the following conditions: 0.1≤λ≤160 and p≥0.1. However, within these ranges of λ and p, the estimates were variable under lower values of λ and p, although the situation improved as n increased. When λ and p are expected to exceed these ranges and the sample size is small, the results suggest that sampling and/or modeling designs should be reconsidered. I then conducted simulation experiments with covariates. I assumed that λ increased with a covariate (x) across 20 sampling sites. I varied p, number of visits (v), and their dependency on a covariate. To compare BMMs with analyses that did not accommodate imperfect detection, I fitted ordinary Poisson generalized linear models to mean and maximum counts (GLMmean and GLMmax). The results showed that GLMmax was superior to GLMmean because GLMmean underestimated λ when p was small. GLMmax underestimated a coefficient of the covariate (slope) when v was negatively correlated with x. BMMs successfully recovered true values of the intercepts, slopes, and λ in most cases. However, when p and v were small, and when p and λ were highly negatively correlated due to their inverse dependency on x, estimates from BMMs were more variable.

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© 2013 The Ornithological Society of Japan
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